NAG Library Routine Document

G01FBF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     TAIL – CHARACTER(1)Input

On entry: indicates which tail the supplied probability represents.

$\mathbf{TAIL}=\text{'U'}$

The upper tail probability, i.e., $P\left(T\ge t_p:\nu \right)$.

$\mathbf{TAIL}=\text{'L'}$

The lower tail probability, i.e., $P\left(T\le t_p:\nu \right)$.

$\mathbf{TAIL}=\text{'S'}$

The two tail (significance level) probability, i.e., $P\left(T\ge \left|t_p\right|:\nu \right)+P\left(T\le -\left|t_p\right|:\nu \right)$.

$\mathbf{TAIL}=\text{'C'}$

The two tail (confidence interval) probability, i.e., $P\left(T\le \left|t_p\right|:\nu \right)-P\left(T\le -\left|t_p\right|:\nu \right)$.

Constraint: $\mathbf{TAIL}=\text{'U'}$, $\text{'L'}$, $\text{'S'}$ or $\text{'C'}$.

2:     P – REAL (KIND=nag_wp)Input

On entry: $p$, the probability from the required Student's $t$-distribution as defined by TAIL.

Constraint: $0.0<\mathbf{P}<1.0$.

3:     DF – REAL (KIND=nag_wp)Input

On entry: $\nu$, the degrees of freedom of the Student's $t$-distribution.

Constraint: $\mathbf{DF}\ge 1.0$.

4:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, because for this routine the values of the output parameters may be useful even if $\mathbf{IFAIL}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry,

$\mathbf{TAIL}\ne \text{'U'}$, $\text{'S'}$, $\text{'C'}$ or $\text{'L'}$.

$\mathbf{IFAIL}=2$

On entry,	$\mathbf{P}\le 0.0$,
or	$\mathbf{P}\ge 1.0$.

$\mathbf{IFAIL}=3$

On entry,

$\mathbf{DF}<1.0$.

$\mathbf{IFAIL}=5$

Convergence in the calculation of the inverse beta value was not achieved. However, the result should be a reasonable approximation to the correct value.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01fbfe.f90)

9.2  Program Data

Program Data (g01fbfe.d)

9.3  Program Results

Program Results (g01fbfe.r)